Comprehensive Collection of Formulas
This document compiles a vast collection of formulas from various areas of mathematics, science, finance, and accounting. Each section below provides the formula in MathJax/LaTeX format along with a brief explanation. Use the table of contents to navigate among the topics.
Table of Contents
- Cosine Law
- Total Debt Formula
- Marginal Cost Formula
- Discount Formula
- Relative Frequency Formula
- Basic Accounting Equation
- Slope-Intercept Formula
- Scale Factor Formula
- Sensitivity Formula
- Gross Profit Percentage Formula
- Hypochlorous Acid Formula
- Profit Formula
- Point-Slope Equation
- X-Intercept Formula
- Population Standard Deviation Formula
- Euler's Formula
- Net Worth Formula
- Money Multiplier Formula
- Percentage Profit Formula
- Arithmetic Sequence Formula
- Exponential Formula
- Arithmetic Series Formula
- Trapezoid Area Formula
- Dental Formula
- Schrödinger Equation
- Sample Standard Deviation Formula
- Variance Formula
- Volume Calculation Formulas
- Tangent Formula
- Cauchy Integral Formula
- Balancing Chemical Equations
- Net Profit Margin Formula
- Parabola Equation
- Physics Equations
- Linear Regression Equation
- Operating Profit Formula
- Percentage Change Formula
- Square Area Formula
- Dividend Payout Ratio Formula
- Beta Formula
- Total Assets Formula
- Total Revenue Formula
- Omega Formula
- Urea Formula
- Turnover Ratio Formula
- DuPont Analysis (ROE)
- Area of a Circle Formula
- Leverage (Debt-to-Equity) Formula
- EBIT Formula
- pH Formula
- Parallelogram Area Formula
- Chemical Formulas
- Net Working Capital Formula
- Correlation Coefficient (r) Formula
- Compounded Monthly Formula
- Debt Ratio Formula
- Net Income Formula
- Current Ratio Formula
- Value at Risk (VaR) Formula
- Interest Coverage Ratio Formula
- Motion Formula
- Power Calculation Formula
- Sample Size Calculation Formula
- Debt-Equity Ratio Formula
- Quick Ratio Formula
- Black-Scholes Formula
- Median Formula for Grouped Data
- Binomial Distribution Formula
- Z Test Formula
- Permutation Formula
- Profitability Ratio Formula
- Ratio and Proportion Formula
- Compound Interest Formula
- Math Formulas for Class 10
- Percentile in Excel
- Geometry Formulas
- Algebra Formulas
- Trigonometry Formulas
- Probability Formulas
- Standard Deviation Formula
Cosine Law
The cosine law relates the sides of a triangle to the cosine of one of its angles:
$$ c^2 = a^2 + b^2 - 2ab\cos(C) $$
Total Debt Formula
Total Debt is often defined as the sum of short‐term and long‐term debt:
$$ \text{Total Debt} = \text{Short-Term Debt} + \text{Long-Term Debt} $$
Marginal Cost Formula
Marginal Cost is the additional cost incurred by producing one extra unit:
$$ MC = \frac{\Delta TC}{\Delta Q} $$
Discount Formula
The discounted price is calculated as the original price multiplied by one minus the discount rate:
$$ \text{Discounted Price} = \text{Original Price} \times (1 - \text{Discount Rate}) $$
Relative Frequency Formula
Relative frequency is the frequency of a given class divided by the total frequency:
$$ \text{Relative Frequency} = \frac{\text{Frequency of Class}}{\text{Total Frequency}} $$
Basic Accounting Equation
The basic accounting equation is fundamental to financial accounting:
$$ \text{Assets} = \text{Liabilities} + \text{Equity} $$
Slope-Intercept Formula
The slope-intercept form of a linear equation is:
$$ y = mx + b $$
Scale Factor Formula
The scale factor is the ratio of the output (or image) size to the original size:
$$ \text{Scale Factor} = \frac{\text{Image Size}}{\text{Original Size}} $$
Sensitivity Formula
Sensitivity measures the change in output per unit change in input:
$$ \text{Sensitivity} = \frac{\Delta \text{Output}}{\Delta \text{Input}} $$
Gross Profit Percentage Formula
Gross Profit Percentage is the ratio of gross profit to revenue expressed as a percentage:
$$ \text{Gross Profit \%} = \frac{\text{Gross Profit}}{\text{Revenue}} \times 100\% $$
Hypochlorous Acid Formula
Hypochlorous acid is chemically represented as:
$$ \mathrm{HOCl} $$
Profit Formula
Profit is defined as the difference between revenue and cost:
$$ \text{Profit} = \text{Revenue} - \text{Cost} $$
Point-Slope Equation
The point-slope form of a line is given by:
$$ y - y_1 = m(x - x_1) $$
X-Intercept Formula
For a line in the form \(y = mx + b\), the x-intercept occurs when \(y=0\):
$$ x = -\frac{b}{m} $$
Population Standard Deviation Formula
The population standard deviation is computed as:
$$ \sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2} $$
Euler's Formula
One of the most famous formulas in mathematics is Euler’s formula:
$$ e^{i\theta} = \cos \theta + i\sin \theta $$
Net Worth Formula
Net Worth is calculated by subtracting liabilities from assets:
$$ \text{Net Worth} = \text{Assets} - \text{Liabilities} $$
Money Multiplier Formula
The money multiplier in banking is given by:
$$ \text{Money Multiplier} = \frac{1}{\text{Reserve Ratio}} $$
Percentage Profit Formula
Percentage profit is calculated as profit divided by cost expressed as a percentage:
$$ \text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost}} \times 100\% $$
Arithmetic Sequence Formula
The nth term of an arithmetic sequence is:
$$ a_n = a_1 + (n-1)d $$
Exponential Formula
An exponential function is often written as:
$$ y = ab^x $$
Arithmetic Series Formula
The sum of the first n terms of an arithmetic sequence is:
$$ S_n = \frac{n}{2}(a_1 + a_n) $$
Trapezoid Area Formula
The area of a trapezoid is:
$$ A = \frac{1}{2}(b_1 + b_2)h $$
Dental Formula
Dental formulas show the number and types of teeth. For example:
Permanent Dentition: \( 2-1-2-3 \) Deciduous Dentition: \( 2-1-0-2 \)
Schrödinger Equation
The time-dependent Schrödinger equation is:
$$ i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2 \psi + V\psi $$
Sample Standard Deviation Formula
The sample standard deviation is given by:
$$ s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2} $$
Variance Formula
Variance for a population and for a sample, respectively:
$$ \sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i-\mu)^2 \quad,\quad s^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2 $$
Volume Calculation Formulas
Examples:
Cube: $$ V = a^3 $$ Sphere: $$ V = \frac{4}{3}\pi r^3 $$
Tangent Formula
The tangent of an angle is the ratio of sine to cosine:
$$ \tan \theta = \frac{\sin \theta}{\cos \theta} $$
Cauchy Integral Formula
In complex analysis, the Cauchy integral formula states:
$$ f(a) = \frac{1}{2\pi i} \oint_{\gamma} \frac{f(z)}{z-a}dz $$
Balancing Chemical Equations
Balancing chemical equations ensures conservation of atoms. For example, the combustion of methane:
$$ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O $$
Net Profit Margin Formula
Net Profit Margin is defined as:
$$ \text{Net Profit Margin} = \frac{\text{Net Profit}}{\text{Total Revenue}} \times 100\% $$
Parabola Equation
The general quadratic form of a parabola is:
$$ y = ax^2 + bx + c $$
Physics Equations
This section collects a few fundamental physics equations. For example, Newton’s second law:
$$ F = ma $$
Linear Regression Equation
The equation for a linear regression line is typically:
$$ \hat{y} = a + bx $$
Operating Profit Formula
Operating profit is calculated as:
$$ \text{Operating Profit} = \text{Total Revenue} - \text{Operating Expenses} $$
Percentage Change Formula
The percentage change from an old value to a new value is:
$$ \% \Delta = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\% $$
Square Area Formula
The area of a square is:
$$ A = s^2 $$
Dividend Payout Ratio Formula
The dividend payout ratio is:
$$ \text{Dividend Payout Ratio} = \frac{\text{Dividends per Share}}{\text{Earnings per Share}} \times 100\% $$
Beta Formula
Beta is calculated as:
$$ \beta = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)} $$
Total Assets Formula
Total Assets are often calculated by summing current and non-current assets:
$$ \text{Total Assets} = \text{Current Assets} + \text{Non-Current Assets} $$
Total Revenue Formula
Total revenue is typically:
$$ TR = P \times Q $$
Omega Formula
In risk analysis, the Omega ratio is defined as:
$$ \Omega = \frac{\text{Probability-weighted gains}}{\text{Probability-weighted losses}} $$
Urea Formula
The chemical formula for urea is:
$$ \mathrm{CO(NH_2)_2} $$
Turnover Ratio Formula
Inventory turnover is calculated as:
$$ \text{Inventory Turnover} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}} $$
DuPont Analysis (ROE)
DuPont’s formula expresses Return on Equity as a product of three ratios:
$$ ROE = \text{Profit Margin} \times \text{Asset Turnover} \times \text{Equity Multiplier} $$
Area of a Circle Formula
The area of a circle is calculated by:
$$ A = \pi r^2 $$
Leverage (Debt-to-Equity) Formula
Leverage is defined as:
$$ \text{Leverage Ratio} = \frac{\text{Total Debt}}{\text{Total Equity}} $$
EBIT Formula
EBIT (Earnings Before Interest and Taxes) is:
$$ EBIT = \text{Total Revenue} - \text{Operating Expenses} $$
pH Formula
pH is defined as the negative logarithm of the hydrogen ion concentration:
$$ \text{pH} = -\log [H^+] $$
Parallelogram Area Formula
The area of a parallelogram is given by:
$$ A = b \times h \quad \text{or} \quad A = ab\sin(\theta) $$
Chemical Formulas
This section can include any additional chemical formulas as needed.
Net Working Capital Formula
Net Working Capital is calculated as the difference between current assets and current liabilities:
$$ \text{NWC} = \text{Current Assets} - \text{Current Liabilities} $$
Correlation Coefficient (r) Formula
The correlation coefficient is computed as:
$$ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} $$
Compounded Monthly Formula
Compound interest compounded monthly is given by:
$$ A = P\left(1 + \frac{r}{12}\right)^{12t} $$
Debt Ratio Formula
The debt ratio is defined as:
$$ \text{Debt Ratio} = \frac{\text{Total Debt}}{\text{Total Assets}} $$
Net Income Formula
Net income is calculated as:
$$ \text{Net Income} = \text{Total Revenue} - \text{Total Expenses} $$
Current Ratio Formula
The current ratio is the ratio of current assets to current liabilities:
$$ \text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} $$
Value at Risk (VaR) Formula
An approximate expression for VaR is:
$$ VaR = \mu - z\sigma $$
Interest Coverage Ratio Formula
The interest coverage ratio is given by:
$$ \text{Interest Coverage} = \frac{EBIT}{\text{Interest Expense}} $$
Motion Formula
For uniformly accelerated motion, the displacement is:
$$ s = ut + \frac{1}{2}at^2 $$
Power Calculation Formula
Power is the rate at which work is done:
$$ P = \frac{W}{t} $$
Sample Size Calculation Formula
A common formula for sample size (for proportions) is:
$$ n = \frac{Z^2 p(1-p)}{E^2} $$
Debt-Equity Ratio Formula
This ratio is calculated as:
$$ \text{Debt-Equity Ratio} = \frac{\text{Total Debt}}{\text{Total Equity}} $$
Quick Ratio Formula
The quick ratio (or acid-test ratio) is:
$$ \text{Quick Ratio} = \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}} $$
Black-Scholes Formula
The Black-Scholes formula for pricing a European call option is:
$$ C = S_0 N(d_1) - X e^{-rT} N(d_2) $$
with
$$ d_1 = \frac{\ln(S_0/X) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}, \quad d_2 = d_1 - \sigma\sqrt{T} $$
Median Formula for Grouped Data
The median for grouped data is estimated as:
$$ \text{Median} = L + \left[\frac{\frac{n}{2} - F}{f}\right] \times c $$
Where \( L \) is the lower boundary of the median class, \( n \) is the total frequency, \( F \) is the cumulative frequency before the median class, \( f \) is the frequency of the median class, and \( c \) is the class width.
Binomial Distribution Formula
The probability of obtaining exactly \( k \) successes in \( n \) trials is given by:
$$ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} $$
Z Test Formula
The Z test statistic is computed as:
$$ z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} $$
Permutation Formula
The number of ways to arrange \( n \) items taking \( r \) at a time is:
$$ P(n, r) = \frac{n!}{(n-r)!} $$
Profitability Ratio Formula
One common profitability measure (Return on Assets) is:
$$ ROA = \frac{\text{Net Income}}{\text{Total Assets}} \times 100\% $$
Ratio and Proportion Formula
If two ratios are equal, then:
$$ \frac{a}{b} = \frac{c}{d} \quad \Longrightarrow \quad ad = bc $$
Compound Interest Formula
Compound interest is calculated as:
$$ A = P\left(1 + \frac{r}{n}\right)^{nt} $$
Math Formulas for Class 10
This section includes various essential formulas for Class 10 mathematics.
Percentile in Excel
In Excel, the function to calculate percentiles is:
=PERCENTILE.EXC(array, k)
Geometry Formulas
This section contains a variety of geometric formulas (area, perimeter, etc.).
Algebra Formulas
This section covers common algebraic identities and equations.
Trigonometry Formulas
This section includes basic trigonometric identities and equations.
Probability Formulas
This section contains formulas used in probability theory.
Standard Deviation Formula
Standard deviation formulas (for both population and sample) have been given above.
Final Thoughts
This extensive document has compiled a vast collection of formulas spanning many areas of mathematics, science, finance, and accounting. Each formula is presented in MathJax/LaTeX format along with a brief explanation. Use the table of contents above to navigate through the topics most relevant to your needs.
Regular review and practice with these formulas will build a solid foundation for further study and application.
Happy calculating, and may this compendium enhance your mathematical and analytical proficiency!
Note: This resource is intended as a comprehensive reference for students, educators, and professionals.
